{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "import sympy as sy\n",
    "sy.init_printing() "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# <font face=\"gotham\" color=\"purple\">Definition of Linear Independence"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If all $c$'s are zero, a set of vectors $\\{v_1, v_2,...,v_p\\}$ is said to be **linearly independent**, if the equation\n",
    "\n",
    "$$c_{1} {v}_{1}+c_{2} {v}_{2}+\\cdots+c_{p} {v}_{p}=\\mathbf{0}$$\n",
    "\n",
    "holds.\n",
    "\n",
    "If any of $c_i\\neq 0$, the set of vectors is linearly dependent."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <font face=\"gotham\" color=\"purple\"> Example 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Determine if ${v}_1, {v}_2, {v}_3$ are linearly independent.\n",
    "$$\n",
    "{v}_{1}=\\left[\\begin{array}{l}\n",
    "1 \\\\\n",
    "2 \\\\\n",
    "3\n",
    "\\end{array}\\right]^T, \n",
    "{v}_{2}=\\left[\\begin{array}{l}\n",
    "4 \\\\\n",
    "5 \\\\\n",
    "6\n",
    "\\end{array}\\right]^T, \\text { and } {v}_{3}=\\left[\\begin{array}{l}\n",
    "2 \\\\\n",
    "1 \\\\\n",
    "0\n",
    "\\end{array}\\right]^T\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The common way of testing linear combination is to construct augmented matrix and calculate the reduced form, for example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left( \\left[\\begin{matrix}1 & 0 & -2 & 0\\\\0 & 1 & 1 & 0\\\\0 & 0 & 0 & 0\\end{matrix}\\right], \\  \\left( 0, \\  1\\right)\\right)$"
      ],
      "text/plain": [
       "⎛⎡1  0  -2  0⎤        ⎞\n",
       "⎜⎢           ⎥        ⎟\n",
       "⎜⎢0  1  1   0⎥, (0, 1)⎟\n",
       "⎜⎢           ⎥        ⎟\n",
       "⎝⎣0  0  0   0⎦        ⎠"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = sy.Matrix([[1,4,2,0],\n",
    "               [2,5,1,0],\n",
    "               [3,6,0,0]])\n",
    "A.rref()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The solution tells that $x_3$ is a free variable, so naturally it could be nonzero because $x_3\\cdot 0 =0$, therefore the set is linearly dependent."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <font face=\"gotham\" color=\"purple\"> Example 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Consider a matrix $A$，determine if columns of $A$ are linearly independent.\n",
    "\n",
    "$$\n",
    "A=\\left[\\begin{array}{rrr}\n",
    "0 & 1 & 4 \\\\\n",
    "1 & 2 & -1 \\\\\n",
    "5 & 8 & 0\n",
    "\\end{array}\\right]\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Solve the system via augmented matrix."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left( \\left[\\begin{matrix}1 & 0 & 0 & 0\\\\0 & 1 & 0 & 0\\\\0 & 0 & 1 & 0\\end{matrix}\\right], \\  \\left( 0, \\  1, \\  2\\right)\\right)$"
      ],
      "text/plain": [
       "⎛⎡1  0  0  0⎤           ⎞\n",
       "⎜⎢          ⎥           ⎟\n",
       "⎜⎢0  1  0  0⎥, (0, 1, 2)⎟\n",
       "⎜⎢          ⎥           ⎟\n",
       "⎝⎣0  0  1  0⎦           ⎠"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = sy.Matrix([[0,1,4,0],[1,2,-1,0],[5,8,0,0]])\n",
    "A.rref()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$Ax=0$ has only trivial solution, i.e. $(c_1, c_2, c_3)^T = (0, 0, 0)$, so the columns of $A$ are linearly independent."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Linear independence is closly connected with linear combination, in next section we visualize the linear independence."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# <font face=\"gotham\" color=\"purple\"> Visualization of Linear Independence"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is a visual example in $\\mathbb{R}^2$, showing $(3, 2)^T$, $(-9, -6)^T$, $(6, 4)^T$ are linearly dependent."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize = (8, 8))\n",
    "#######################Arrows#######################\n",
    "arrows = np.array([[[0,0,3,2]],\n",
    "                   [[0,0,-9,-6]], \n",
    "                   [[0,0,6,4]]])\n",
    "colors = ['r','b','g']\n",
    "for i in range(arrows.shape[0]):\n",
    "    X,Y,U,V = zip(*arrows[i,:,:])\n",
    "    ax.arrow(X[0], Y[0], U[0],V[0], color = colors[i], width = .18, \n",
    "             length_includes_head = True,\n",
    "             head_width = .3, # default: 3*width\n",
    "             head_length = .6,\n",
    "             overhang = .4, zorder = -i)\n",
    "\n",
    "ax.scatter(0, 0, ec = 'red', fc = 'black', zorder = 5)\n",
    "ax.text(6, 4, '$(6, 4)$')\n",
    "ax.text(-9, -6.5, '$(-9, -6)$')\n",
    "ax.text(3, 2, '$(3, 2)$')\n",
    "\n",
    "ax.grid(True)\n",
    "ax.set_title('Linear Dependence Visualization')\n",
    "ax.axis([-10, 10, -10, 10])\n",
    "ax.set_xlabel('x-axis', size = 18)\n",
    "ax.set_ylabel('y-axis', size = 18)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Simply put, _if one vector is the scalar multiple of the other vector, e.g. $3u = v$, these two vectors are linearly dependent_."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we visualize linear independence in $\\mathbb{R}^3$ with vectors $(1,-2,1)^T$, $(2,1,2)^T$, $(-1,2,3)^T$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The standard procedure is to write down the span of first two vectors, which is a plane. Then we examine whether the third vector is in the plane. If not, this set of vectors is linearly independent.\n",
    "\n",
    "$$\n",
    "\\left[\n",
    "\\begin{matrix}\n",
    "x\\\\\n",
    "y\\\\\n",
    "z\n",
    "\\end{matrix}\n",
    "\\right]=\n",
    "s\\left[\n",
    "\\begin{matrix}\n",
    "1\\\\\n",
    "-2\\\\\n",
    "1\n",
    "\\end{matrix}\n",
    "\\right]+\n",
    "t\\left[\n",
    "\\begin{matrix}\n",
    "2\\\\\n",
    "1\\\\\n",
    "2\n",
    "\\end{matrix}\n",
    "\\right]=\n",
    "\\left[\n",
    "\\begin{matrix}\n",
    "s+2t\\\\\n",
    "-2s+t\\\\\n",
    "s+2t\n",
    "\\end{matrix}\n",
    "\\right]\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# %matplotlib notebook, use this only when you are in Jupyter Notebook, it doesn't work in Jupyterlab\n",
    "fig = plt.figure(figsize = (10,10))\n",
    "ax = fig.add_subplot(projection='3d')\n",
    "\n",
    "s = np.linspace(-1, 1, 10)\n",
    "t = np.linspace(-1, 1, 10)\n",
    "S, T = np.meshgrid(s, t)\n",
    "\n",
    "X = S+2*T\n",
    "Y = -2*S+T\n",
    "Z = S+2*T\n",
    "ax.plot_wireframe(X, Y, Z, linewidth = 1.5, color = 'k', alpha = .6)\n",
    "\n",
    "vec = np.array([[[0, 0, 0, 1, -2, 1]],\n",
    "               [[0, 0, 0, 2, 1, 2]],\n",
    "               [[0, 0, 0, -1, 2, 3]]])\n",
    "colors = ['r','b','g']\n",
    "for i in range(vec.shape[0]):\n",
    "    X, Y, Z, U, V, W = zip(*vec[i,:,:])\n",
    "    ax.quiver(X, Y, Z, U, V, W, length=1, normalize=False, color = colors[i],\n",
    "              arrow_length_ratio = .08, pivot = 'tail',\n",
    "              linestyles = 'solid',linewidths = 3, alpha = .6)\n",
    "\n",
    "ax.set_title('Linear Independence Visualization')\n",
    "\n",
    "ax.set_xlabel('x-axis', size = 18)\n",
    "ax.set_ylabel('y-axis', size = 18)\n",
    "ax.set_zlabel('z-axis', size = 18)\n",
    "\n",
    "ax.view_init(elev=50., azim=0)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Pan around the image (either by setting ```ax.view_init``` or using JupyterLab widget), we can see that the <font face=\"gotham\" color=\"green\">green</font> vector is not in the plane spanned by <font face=\"gotham\" color=\"red\">red</font> and <font face=\"gotham\" color=\"blue\">blue</font> vector, thus they are linearly independent."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div style=\"background-color:Bisque; color:DarkBlue; padding:30px;\">\n",
    "<b>A Sidenote About Linear Independence</b><br><br>\n",
    "Let $S = \\{{v}_1,{v}_2,{v}_3, ..., {v}_n\\}$ be a set of vectors in $\\mathbb{R}^m$, if $n>m$, then $S$ is always linearly dependent. Simple example is $4$ vectors in $\\mathbb{R}^3$, even if $3$ of them are linearly independent, the $4$th one can never be independent of them. <br><br>\n",
    "\n",
    "Also if $S = \\{{v}_1,{v}_2,{v}_3, ..., {v}_n\\}$ contains a zero vector, then the set is always linearly dependent.\n",
    "</div> "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
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